Try adjusting the height of your bridge too.
If it's too high, your fingers will slide under the other strings.
If it's too low, you'll push the other strings downwards onto the fretboard.
Ideally, you want to have it so that when you bend, you're pushing the other strings out of the way. (you still have to mute the other strings tho)

If you adjust your bridge height, don't forget to reset the intonation.